Is (2, 9) a solution to the following system of equations? y = 3x + 3 , y = 4x + 1
Understand the Problem
The question is asking if the coordinate (2,9) is a solution to the given system of equations. To determine this, we need to substitute x=2 and y=9 into both equations. If both equations are true after the substitution, then (2,9) is a solution. Otherwise, it is not a solution.
Answer
yes
Answer for screen readers
yes
Steps to Solve
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Substitute x=2 and y=9 into the first equation We have the first equation $y = 3x + 3$. Substituting $x=2$ and $y=9$, we get $9 = 3(2) + 3$.
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Simplify the first equation Simplify the right side of the equation: $3(2) + 3 = 6 + 3 = 9$. Thus, $9 = 9$. The first equation is true.
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Substitute x=2 and y=9 into the second equation We have the second equation $y = 4x + 1$. Substituting $x=2$ and $y=9$, we get $9 = 4(2) + 1$.
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Simplify the second equation Simplify the right side of the equation: $4(2) + 1 = 8 + 1 = 9$. Thus, $9 = 9$. The second equation is true.
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Determine if (2,9) is a solution Since both equations are true when $x=2$ and $y=9$, the point (2,9) is a solution to the system of equations.
yes
More Information
A solution to a system of equations must satisfy all equations in the system.
Tips
A common mistake is to only check one equation. To be a solution to the system, the point must satisfy all equations in the system.
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